ANALYSIS OF AN INHOMOGENEOUS GENERALIZED EPSTEIN-HURWITZ ZETA-FUNCTION WITH PHYSICAL APPLICATIONS

The inhomogeneous generalized (Epstein-Hurwitz-like) multidimensional series E(m)(s; a1,...,a(m);c1,...,c(m);c2) = SIGMA(n1,...,n(m) infinit y = 0 [a1(n1 + c1)2 + ... + a(m)(n(m) + c(m))2 + c2]-s is investigated . By means of a nontrivial, asymptotic recurrence, it is reduced to th e one-dimensional case F(s; a,b2) = SIGMA(n=0)infinity[(n + a)2 + b2]- s, which is then studied in full detail. In particular, asymptotic exp ansions for F and its derivatives partial-derivativeF/partial-derivati ve and partial-derivativeF/partial-derivativea-together with analytica l continuations of the same in the variable s-are explicitly obtained using zeta-function techniques. Several plots and tables of the numeri cal results are given. Some explicit applications to the regularizatio n, by means of Hurwitz zeta-functions, of different problems that have appeared recently in the physical literature, are considered.